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Use of Silicone Materials to Simulate Tissue Biomechanics as Related to Deep Tissue Injury Jessica L. Sparks, PhD; Nicholas A. Vavalle, MS; Krysten E. Kasting; Benjamin Long, MS; Martin L. Tanaka, PhD; Phillip A. Sanger, PhD; Karen Schnell, MSN; and Teresa A. Conner-Kerr, PhD ABSTRACT OBJECTIVE: Deep tissue injury (DTI) is caused by prolonged mechanical loading that disrupts blood flow and metabolic clearance. A patient simulator that mimics the biomechanical aspects of DTI initiation, stress and strain in deep muscle tissue, would be potentially useful as a training tool for pressure-relief techniques and testing platform for pressure-mitigating products. As a step toward this goal, this study evaluates the ability of silicone materials to mimic the distribution of stress in muscle tissue under concentrated loading. METHODS: To quantify the mechanical properties of candidate silicone materials, unconfined compression experiments were conducted on 3 silicone formulations (Ecoflex 0030, Ecoflex 0010, and Dragon Skin; Smooth-On, Inc, Easton, Pennsylvania). Results were fit to an Ogden hyperelastic material model, and the resulting shear moduli (G) were compared with published values for biological tissues. Indentation tests were then conducted on Ecoflex 0030 and porcine muscle to investigate silicone’s ability to mimic the nonuniform stress distribution muscle demonstrates under concentrated loading. Finite element models were created to quantify stresses throughout tissue depth. Finally, a preliminary patient simulator prototype was constructed, and both deep and superficial ‘‘tissue’’ pressures were recorded to examine stress distribution. RESULTS: Indentation tests showed similar stress distribution trends in muscle and Ecoflex 0030, but stress magnitudes were higher in Ecoflex 0030 than in porcine muscle. All 3 silicone formulations demonstrated shear moduli within the range of published values for biological tissue. For the experimental conditions reported in this work, Ecoflex 0030 exhibited greater stiffness than porcine muscle. CONCLUSION: Indentation tests and the prototype patient simulator trial demonstrated similar trends with high pressures closest to the bony prominence with decreasing magnitude toward the interfacial surface. Qualitatively, silicone mimicked the phenomenon observed in muscle of nonuniform stress under concentrated loading. Although shear moduli were within biological ranges, stress and stiffness values exceeded those of porcine muscle. This research represents a first step toward development of a preclinical model simulating the biomechanical conditions of stress and strain in deep muscle, since local biomechanical factors are acknowledged to play a role in DTI initiation. Future research is needed to refine the capacity of preclinical models to simulate biomechanical parameters in successive tissue layers of muscle, fat, dermis, and epidermis typically intervening between bone and support surfaces, for body regions at risk for DTI. KEYWORDS: deep tissue injury, soft tissue biomechanics, pressure ulcer, patient simulator ADV SKIN WOUND CARE 2015;28:59Y68 INTRODUCTION Pressure ulcers (PrUs) are a common condition in both persons who use wheelchairs and those unable to sit out of bed. They cost the United States alone more than $1.2 billion 1 and affect 10% of all hospitalized patients. 2 Pressure ulcers can be broadly classified as 1 of 2 types: superficial or deep. 3 Superficial ulcers affect skin layers near the epidermis and are formed as a result of damaging frictional and shear forces in the presence of moisture and heat. 3,4 Deep PrUs are the focus of this study. These ulcers develop in deep muscle tissue next to bony prominences such as the sacrum, ADVANCES IN SKIN & WOUND CARE & FEBRUARY 2015 59 WWW.WOUNDCAREJOURNAL.COM ORIGINAL INVESTIGATION Jessica L. Sparks, PhD, is an Associate Professor of Chemical, Paper, and Biomedical Engineering, Miami University, Oxford, Ohio. Nicholas A. Vavalle, MS, is a doctoral candidate in biomedical engineering, Wake Forest University, Winston-Salem, North Carolina. Krysten E. Kasting is a bioengineering undergraduate student, Miami University, Oxford, Ohio. Benjamin Long, MS, is an Instructor of Physical Therapy, Winston-Salem State University, Winston-Salem, North Carolina. Martin L. Tanaka, PhD, is an Assistant Professor of Engineering and Technology, Western Carolina University, Cullowhee, North Carolina. Phillip A. Sanger, PhD, is a Professor of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana. Karen Schnell, MSN, owns Blue Sky Health Concepts Consulting, Mebane, North Carolina. Teresa A. Conner-Kerr, PhD, is Dean of the College of Health Sciences, University of North Georgia, Dahlonega, Georgia. Dr Sparks and Mr Vavalle have disclosed that Wake Forest University is a past recipient of grant funding from the US Department of Education (awarded to T.A.C.-K.). Mr Long has disclosed that Winston-Salem State University is a past recipient of grant funding from the US Department of Education (awarded to T.A.C.-K.). Dr Sanger has disclosed that his institution is a past recipient of grant funding from the Golden Leaf Foundation. Ms Schnell has disclosed that she has previously received an honorarium from Winston-Salem State University, and is a past recipient of payment for writing or reviewing a manuscript from Winston-Salem State University. Dr Kerr has disclosed that Winston-Salem State University is a past recipient of a Title III US Department of Education grant. Ms Kasting and Dr Tanaka have disclosed that they have no financial relationships related to this article. Acknowledgments: The authors acknowledge Nick Ashworth, Isaac Crisp, Andrew York, and Erik Ellington for their assistance with data acquisition and graphical user interface development. The authors also thank Kristen Pone, Christen Isley, and Peggy Furr, for their assistance with fiberglass casting and material acquisition. Funding for this research was provided by the US Department of Education (grant P031B085015-9 to T.A.C.-K.) and the Goldenleaf Fund (to P.A.S.). Submitted July 5, 2013; accepted in revised form April 2, 2014. Copyright © 2015 Wolters Kluwer Health | Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

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Page 1: Use of Silicone Materials to Simulate Tissue …wcu.edu/WebFiles/PDFs/KS_Sparks_Tanaka.pdfUse of Silicone Materials to Simulate Tissue Biomechanics as Related to Deep Tissue Injury

Use of Silicone Materials to Simulate TissueBiomechanics as Related to Deep Tissue Injury

Jessica L. Sparks, PhD; Nicholas A. Vavalle, MS; Krysten E. Kasting; Benjamin Long, MS; Martin L. Tanaka, PhD;Phillip A. Sanger, PhD; Karen Schnell, MSN; and Teresa A. Conner-Kerr, PhD

ABSTRACTOBJECTIVE: Deep tissue injury (DTI) is caused by prolonged

mechanical loading that disrupts blood flow and metabolic

clearance. A patient simulator that mimics the biomechanical

aspects of DTI initiation, stress and strain in deep muscle tissue,

would be potentially useful as a training tool for pressure-relief

techniques and testing platform for pressure-mitigating products.

As a step toward this goal, this study evaluates the ability of

silicone materials to mimic the distribution of stress in muscle

tissue under concentrated loading.

METHODS: To quantify the mechanical properties of candidate

silicone materials, unconfined compression experiments were

conducted on 3 silicone formulations (Ecoflex 0030, Ecoflex 0010,

and Dragon Skin; Smooth-On, Inc, Easton, Pennsylvania). Results

were fit to an Ogden hyperelastic material model, and the resulting

shear moduli (G) were compared with published values for

biological tissues. Indentation tests were then conducted on

Ecoflex 0030 and porcine muscle to investigate silicone’s ability to

mimic the nonuniform stress distribution muscle demonstrates under

concentrated loading. Finite elementmodelswere created to quantify

stresses throughout tissue depth. Finally, a preliminary patient

simulator prototype was constructed, and both deep and superficial

‘‘tissue’’ pressures were recorded to examine stress distribution.

RESULTS: Indentation tests showed similar stress distribution

trends in muscle and Ecoflex 0030, but stress magnitudes were

higher in Ecoflex 0030 than in porcine muscle. All 3 silicone

formulations demonstrated shear moduli within the range of

published values for biological tissue. For the experimental

conditions reported in this work, Ecoflex 0030 exhibited greater

stiffness than porcine muscle.

CONCLUSION: Indentation tests and the prototype patient

simulator trial demonstrated similar trends with high pressures

closest to the bony prominence with decreasing magnitude toward

the interfacial surface. Qualitatively, silicone mimicked the

phenomenon observed in muscle of nonuniform stress under

concentrated loading. Although shear moduli were within

biological ranges, stress and stiffness values exceeded those of

porcine muscle. This research represents a first step toward

development of a preclinical model simulating the biomechanical

conditions of stress and strain in deep muscle, since local

biomechanical factors are acknowledged to play a role in DTI

initiation. Future research is needed to refine the capacity of

preclinical models to simulate biomechanical parameters in

successive tissue layers of muscle, fat, dermis, and epidermis

typically intervening between bone and support surfaces, for body

regions at risk for DTI.

KEYWORDS: deep tissue injury, soft tissue biomechanics,

pressure ulcer, patient simulator

ADV SKIN WOUND CARE 2015;28:59Y68

INTRODUCTIONPressure ulcers (PrUs) are a common condition in both persons

who use wheelchairs and those unable to sit out of bed. They cost

the United States alone more than $1.2 billion1 and affect 10% of

all hospitalized patients.2 Pressure ulcers can be broadly classified

as 1 of 2 types: superficial or deep.3 Superficial ulcers affect skin

layers near the epidermis and are formed as a result of damaging

frictional and shear forces in the presence of moisture and heat.3,4

Deep PrUs are the focus of this study. These ulcers develop in

deepmuscle tissue next to bony prominences such as the sacrum,

ADVANCES IN SKIN & WOUND CARE & FEBRUARY 201559WWW.WOUNDCAREJOURNAL.COM

ORIGINAL INVESTIGATION

Jessica L. Sparks, PhD, is an Associate Professor of Chemical, Paper, and Biomedical Engineering, Miami University, Oxford, Ohio. Nicholas A. Vavalle, MS, is a doctoral candidate in biomedical

engineering, Wake Forest University, Winston-Salem, North Carolina. Krysten E. Kasting is a bioengineering undergraduate student, Miami University, Oxford, Ohio. Benjamin Long, MS, is an

Instructor of Physical Therapy,Winston-SalemState University, Winston-Salem, North Carolina.Martin L. Tanaka, PhD, is an Assistant Professor of Engineering and Technology,Western Carolina

University, Cullowhee, NorthCarolina. PhillipA. Sanger, PhD, is a Professor of Electrical andComputer Engineering, PurdueUniversity,West Lafayette, Indiana. Karen Schnell,MSN, ownsBlueSky

Health Concepts Consulting, Mebane, North Carolina. Teresa A. Conner-Kerr, PhD, is Dean of the College of Health Sciences, University of North Georgia, Dahlonega, Georgia. Dr Sparks

and Mr Vavalle have disclosed that Wake Forest University is a past recipient of grant funding from the US Department of Education (awarded to T.A.C.-K.). Mr Long has disclosed that

Winston-Salem State University is a past recipient of grant funding from the US Department of Education (awarded to T.A.C.-K.). Dr Sanger has disclosed that his institution is a past

recipient of grant funding from the Golden Leaf Foundation. Ms Schnell has disclosed that she has previously received an honorarium fromWinston-Salem State University, and is a past

recipient of payment for writing or reviewingamanuscript fromWinston-SalemStateUniversity.DrKerr hasdisclosed thatWinston-SalemStateUniversity is apast recipientof aTitle IIIUSDepartment

of Educationgrant.MsKasting andDr Tanaka havedisclosed that they haveno financial relationships related to this article.Acknowledgments:The authors acknowledgeNickAshworth, IsaacCrisp,

AndrewYork, and Erik Ellington for their assistancewith data acquisition and graphical user interface development. The authors also thank Kristen Pone, Christen Isley, and Peggy Furr, for their

assistance with fiberglass casting andmaterial acquisition. Funding for this research was provided by the US Department of Education (grant P031B085015-9 to T.A.C.-K.) and the Goldenleaf

Fund (to P.A.S.). Submitted July 5, 2013; accepted in revised form April 2, 2014.

Copyright © 2015 Wolters Kluwer Health | Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

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ischial tuberosity, or greater trochanter of the femur.3,5,6 Deep PrUs

are caused by prolonged mechanical loading (compression) that

interferes with blood flow and clearance of metabolic byproducts.

As the deep muscle tissue undergoes necrosis, it becomes stiffer,

projecting themechanical stresses tomore superficial tissues, which

then bear the mechanical load.7,8 Since the injury develops under

intact skin, the damage is difficult to detect at early stages. These

potentially life-threatening injuries have been termed deep tissue

injury (DTI).9

Biomechanical research6,10 has demonstrated that concentrated

stresses in deep tissues near bony prominences cannot be readily

predicted from surface pressuremaps, which are currently a key

technology for pressure-related risk assessment.3,11 Since DTIs de-

velop deep in the subdermal tissue layer, the use of interfacial

pressure mapping to evaluate clinical strategies for DTI preven-

tion, such as cushions, mattresses, and repositioning techniques,

can be misleading.6,12,13 If clinicians could more accurately eval-

uate the stresses that developwithin deepmuscle tissue, they could

provide better information to healthcare providers regarding the

ability of repositioning protocols to lessen the localmechanical load

at deep, high-risk sites. In addition, clinicians could generate better

test protocols for evaluating the effectiveness of pressure-relieving

products, such asmattress and cushions, for DTI prevention. These

goals can potentially be achieved in the long term by developing a

novel patient simulator with biomechanical properties similar to

actual human tissues, including compressive properties of muscle

tissue and stresses near the bone-muscle interface.

Although a variety of buttock phantoms have been developed

for wheelchair-cushion testing, few of these32,33 generate informa-

tion regarding the stress or deformation of deepermaterial adjacent

to a simulated ‘‘bone.’’ Those that have been reported were made

of polyvinyl chloride cast around a wooden core and thus lacked

realistic mechanical properties of biological tissues.32,33

Because the composition andmicrostructure of biological tissue

are enormously complex, the construction of a suitably accurate

simulator for DTI prevention is a significant challenge. The long-

term goal of this work is the development of a simulator that

mimics the biomechanical conditions of stress and strain in deep

muscle, since local biomechanical factors are acknowledged to

play a role in DTI initiation.6Y8,34,35 As a step toward this goal, this

study evaluates the ability of soft silicone materials to mimic spe-

cific features of the compressivemechanical behavior of biological

muscle tissue. In particular, this study will focus on (1) shear mod-

ulus, a mechanical property indicative of how stiff a material feels

to the touch, and (2) the ability of a material to mimic the non-

uniform stress distribution in tissues subjected to indentation-

type loading, such as thatwhich occurs inmuscle compressed by a

bony prominence. Thesematerial features are expected to be among

the relevant features necessary for reproducing, in a synthetic

environment, the biomechanical conditions associated with DTI

initiation. Silicone rubber was selected as a good candidate ma-

terial for this initial study because of its ability to retain its shape

and its resistance to degradation and because it can be readily ob-

tained indifferentdegreesof stiffness tomimicmechanical properties

of biological tissue.

The objectives of the study are as follows:� Measure the mechanical properties for 3 formulations of silicone

using uniaxial unconfined compression experiments, and compare

resulting shear moduli to published values for biological tissues

(muscle, fat, and skin) tested in compression.� Using an indenter with realistic bony geometry, conduct inden-

tation experiments in both silicone and muscle tissue specimens

and examine how pressure varies as a function of distance from

the bony prominence (indenter tip).� Demonstrate proof of principle that a prototype patient simu-

lator can be used to obtain internal pressure measurements at

multiple tissue depths near a specified bony prominence.

METHODSBiomechanical TestingSpecimen Preparation. Three formulations of silicone rubber were

obtained from Smooth-On, Inc (Easton, Pennsylvania): Dragon

Skin, Ecoflex 0010, and Ecoflex 0030. Cylindrical samples (average

diameter, 35.8 mm; average height, 24.5 mm) were prepared ac-

cording to themanufacturer’s specifications for uniaxial compres-

sion tests by mixing the appropriate 2-part liquid forms of each

formulation together and pouring the mixture into a mold. They

were then allowed to cure for the recommended amount of time

(75minutes forDragon Skin, 4 hours for each Ecoflex). During the

curing phase, a level was used to verify that the top and bottom of

each sample were parallel, in order to avoid asymmetric loading

during the uniaxial compression test. For this test series, a total of

18 specimens were produced, 6 of each type of rubber. Each spec-

imenwasmeasuredwith calipersafterdemolding toensure consistent

dimensions.

An additional set of 3 Ecoflex 0030 samples (average diameter,

59.3 mm; average height, 26 mm) were prepared for indentation

testing using the same preparation methods. Samples of porcine

muscle obtained fromthe local grocerwere alsoprepared toundergo

similar testing. Six porcine muscle samples were prepared as cylin-

ders (average diameter, 60.2 mm; average height, 28.2 mm). The

specimenswere presliced to uniform thickness, and sampleswere

cut using a circular guide and surgical blade.

Uniaxial Unconfined Compression. Uniaxial unconfined compres-

sion testing is a standardized method for evaluating the mech-

anical properties of compliant materials, such as polymers or soft

tissues.14 Uniaxial compression tests were conducted for each sili-

cone specimen using an Electroforce LM1 Test Bench mechanical

ADVANCES IN SKIN & WOUND CARE & VOL. 28 NO. 2 60 WWW.WOUNDCAREJOURNAL.COM

ORIGINAL INVESTIGATION

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testing system (Bose Corporation, Eden Prairie, Minnesota) with

a 250-N capacity load cell. The uniaxial compression test con-

sisted of loading the specimen at a constant rate (1.0% strain per

second)until the selectedmaximumstrain value (25%compression)

was reached. The strain rate andmaximumstrain valueswere chosen

to reflect test conditions that have been previously reported for

biological tissues tested in compression.15,16 Force and displace-

ment data were recorded in all tests. Force data were converted to

engineering stress by dividing by the initial cross-sectional area of

the specimen. Displacement data were used to calculate engineer-

ing strain as change in length divided by original length. The

experimental setup was identical for all 3 silicone formulations.

Petroleum jelly was applied to the top and bottom of each sample

before testing to reduce the effects of friction.

Indentation Testing. For the indentation experiments, a human

sacrum model (3B Scientific, Tucker, Georgia) was mounted to

the Bose Electroforce LM1 Test Bench mechanical testing system

using a custom-mounting fixture (Figure 1). The spinous tubercle

of the bone model was used to indent the specimens. Prior to

indentation, 2 Millar Mikro-Tip Pressure Catheters (SPR-524;

ADInstruments, Colorado Springs, Colorado) were inserted into

the specimens at 2 or 5 mm from the top and bottom surfaces of

the specimen, for porcine muscle and Ecoflex 0030 samples, re-

spectively. Pressure sensor locations were termed deep (near the

bonyprominence) andsuperficial (distant fromthebonyprominence)

(Figure 1). A needle was used to create guide holes for sensor in-

sertion, and the guide holes were prefilled with petroleum jelly to

create a smooth coupling between the specimens andminiature pres-

sure sensors. The indentation test consisted of loading the specimen

at a constant rate of 0.5 mm/s for 8 seconds. Force and pressure (at

both deep and superficial depths) data were recorded in all tests.

Patient Simulator Prototype. Based on the results of the material

characterization experiments (Tables 1 and 2), Dragon Skin was

used asmuscle, Ecoflex 0010 as fat, and Ecoflex 0030 as skin in the

initial simulator prototype. The prototype design was based on

approximate human anatomical structure of the pelvis and upper

thigh (Figure 2). The external geometry of the simulatorwas formed

using a fiberglass cast from waist to midthigh. The inside of the

fiberglass mold was coated with a thin layer of plaster to allow for

easy removal of the silicone after molding. A thin layer of the skin

simulant material was ‘‘painted’’ on the plaster and ultimately

formed the outer surface of the simulator prototype. Simulated

muscles were created by pouring muscle simulant into separate

molds thatwere previously constructed tomimic the approximate

shape of the major muscles of the pelvis and hip region. The mus-

cles were affixed to the bony pelvis (Human Skeleton Model; 3B

Scientific) in the corresponding anatomical locations. The bony

pelvis with attached muscles was then suspended inside the fiber-

glass mold in the appropriate anatomical orientation. Simulated fat

material (in liquid form) was then poured into the mold, to fill the

spaces between the skin layer and themuscles. The fatmaterial was

allowed to solidify.

The completed simulator prototype, shown in Figure 2, was

designed to determinewhether it is feasible to produce and detect

differences in deep internal pressures (near a bony prominence)

Figure 1.

INDENTATION TEST SETUP FOR PORCINE MUSCLEWITH

CUSTOM-MOUNTED3BSCIENTIFICSACRUMBONEINDENTER

Load cell and both deep and superficial Millar Mikro-Tip Pressure Catheters are labeled.

Table 1.

LITERATURE RANGES FOR SHEAR MODULIOF BIOLOGICAL TISSUES: ALL DATAREPORTED FROM COMPRESSION TESTING

Biological Tissue G (kPa)

Muscle Longitudinal 51Y10523Y25

Transverse 11Y5423,25

Active 17.1Y30.522,25

Relaxed 4.6Y23.86,15,16,22

Skin 2.8Y31.96,20,26

Fat 1.9Y31.96,20,26

Table 2.

BEST-FIT HYPERELASTIC MATERIALCONSTANTS FOR SILICONE RUBBERFORMULATIONS

Silicone Type

Ogden Model Terms

Poisson Ratio M

Shear ModulusG (kPa)

Strain HardeningExponent >

Dragon Skin 75.449 5.836 0.4999Ecoflex 0010 12.605 4.32 0.4999Ecoflex 0030 22.081 0.825 0.4999

ADVANCES IN SKIN & WOUND CARE & FEBRUARY 201561WWW.WOUNDCAREJOURNAL.COM

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and more superficial pressures (closer to the skin surface) in sim-

ulated soft tissues. Internal pressure data can be transferred from

the simulator to the computer, exhibited on screen for immediate

feedback, and stored for future analysis (Figure 2C). In a preliminary

trial, the simulator was instrumented with 2Millar Mikro-Tip Pres-

sure Catheters (Millar, Inc, Houston, Texas) using the needle-guided

insertion technique described above. One pressure sensor was in-

serted in deep tissue adjacent to the spinous tubercle of the sacrum.

The second sensor was also inserted over the spinous tubercle but

in more superficial tissue just beneath the skin. Manual pressure

was then applied with an open palm over the instrumented region,

and pressures recorded from both sensors.

Figure 2.

PRELIMINARY SIMULATOR PROTOTYPE

A, Simulator prototype instrumented with pressure transducers at both deep and superficial locations over the sacrum. B, Computed tomography scan of prototype showing skeletalanatomy. C, Simulator control software and user interface.

Figure 3.

ECOFLEX 0030 FINITE ELEMENT MODEL AT MAXIMUM INDENTATION

A, Color mapping shows the normal stress distribution through the sample. B, Pressure related to distance from the indenter along line LS of the model.

ADVANCES IN SKIN & WOUND CARE & VOL. 28 NO. 2 62 WWW.WOUNDCAREJOURNAL.COM

ORIGINAL INVESTIGATION

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Finite Element ModelingComputational finite element (FE) simulations were developed

to create virtual (in silico) models of both types of mechanical

tests: uniaxial unconfined compression and indentation. Models

of uniaxial unconfined compression were used to determine the

mechanical properties (Table 2 and Appendix) for each silicone

formulation, by fitting hyperelastic Ogden model parameters to

the average experimental stress-strain results for each silicone for-

mulation. The calculated silicone mechanical properties were then

implemented in separate FE simulations of the silicone indentation

experiments. Analogous simulations of the porcinemuscle inden-

tation experiments were also created, using previously published

and validated mechanical property values for muscle.17

The computer simulations of the indentation experiments were

used to quantify the expected stress everywhere in the specimen,

from immediately adjacent to the spinous tubercle indenter to the

most distant regions from the indenter tip. The models were also

used to examine how the stresses in the specimen variedwith time,

from initial indenter contact until peak indentation was achieved.

To validate these model-predicted stress distributions, model output

was compared directly against the measured ‘‘deep’’ and ‘‘super-

ficial’’ pressure values, which were recorded at known depths in

the sample throughout the indentation (Figures 3 and 4). Results of

these comparisons were used to verify the accuracy of the models.

Details of the FEmodel development are provided in theAppendix.

Statistical AnalysisTo assess the accuracy of the mechanical property values imple-

mented in the FE simulations for each synthetic tissue analog,

linear regression analyses of model output versus experimental

values were conducted for each simulation.18 A slope value near

unity indicated a one-to-one relationship between experiment and

model, and anR2 value near unity indicated a high goodness of fit.

RESULTSFE Model ParametersBest-fit material constants for all silicone rubber formulations are

given in Table 2.Material constants formuscle17 are given in Table 3.

Experimental Results and FE Model ValidationUniaxial Unconfined Compression. The measured peak stresses for

DragonSkin,Ecoflex0010,andEcoflex0030were73.0T 5.2,12.1T 0.75,

and 24.0 T 1.7 kPa, respectively (mean T 1 SD). Stress versus strain

results are illustrated in Figure 5, showing experimental data com-

pared with best-fit FE model results for all silicone formulations.

Linear regression (models vs experiments) of the ramp phase

of compression showed high goodness of fit (R2 = 0.999), with

slope values at or near unity (slope = 0.99Y1.00, P G .05). These

results indicate a good fit of the models to the experimental data,

giving confidence in the accuracy of the material property values

(Table 2) implemented in the models.

Figure 4.

PORCINE MUSCLE FINITE ELEMENT MODEL AT MAXIMUM INDENTATION

A, Color mapping shows the normal stress distribution through the sample. B, Pressure related to distance from the indenter along the line LM of the model.

ADVANCES IN SKIN & WOUND CARE & FEBRUARY 201563WWW.WOUNDCAREJOURNAL.COM

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Comparison with Biological Tissues. Table 2 shows a summary

of the shear modulus values of the 3 silicone rubber formulations,

which can be compared against a range of shear moduli for mus-

cle, fat, and skin tissues found in the literature (Table 1). Biological

tissue shear moduli were taken only from studies in which the tis-

sueswere tested in compression, because biomechanical property

data can vary significantly depending on the test mode used. The

shear moduli of all silicone materials evaluated in the present study

fell within the range of reported values for shear moduli of muscle,

fat, and skin, for biomechanical tests conducted in compression.

IndentationTesting. The model-predicted stress distributions in

the tissue, at maximum indentation, are shown in Figures 3A and

4A for Ecoflex 0030 and for porcine muscle, respectively. Model

results are presented as normal compressive stress (S22) in the

direction of loading. Stresses were then converted to units of milli-

meters of mercury to facilitate comparison against pressuresmea-

sured experimentally at 2 locations per specimen: deep (near the

indenter) and superficial (opposite the indenter).

Similar stress distribution patterns can be seen in the Ecoflex

0030 and porcinemuscle (Figures 3B and 4B)with highest stresses

located adjacent to the bony prominence and with a lessening

degree farther from the prominence. However, the Ecoflex 0030

material showed much greater stress magnitudes compared with

muscle tissue. Experimental data showedgoodagreementwith these

trends. Ecoflex 0030 had an averagemeasured peak deep pressure

(near the indenter) of 142.5mmHg and an averagemeasured peak

superficial pressure (opposite the indenter) of 18.0mmHg,whereas

the porcinemuscle demonstrated an average peak deep pressure of

20.0 mm Hg and average superficial peak pressure of 2.4 mm Hg.

Figures 3 and 4 provide direct comparisons of the experimental

pressures recorded at known locations in the sample atmaximum

indentation, with the FEmodel predictions of stress at these same

locations. Results suggest that the virtual FE models of indentation

provide a good representation of the stress distributions produced

Table 3.

HYPERELASTIC MATERIAL CONSTANTS FORMUSCLE USED IN FE SIMULATIONS17

[-] kPa kPa-1

>1=0.1316402E+01 K1=1.02571 D1=0.194987E-01>2=0.1835933E+02 K2=0.145209 E-04 D2=0.166315

Note: For this material, D1 = 0.194987E-01 kPa-1 is equivalent to Poisson’s ratio M = .495.

Figure 5.

RESULTS OF UNIAXIAL COMPRESSION TESTS ON SILICONE RUBBERS (DRAGON SKIN, ECOFLEX 0010, AND ECOFLEX

0030) COMPARED WITH FINITE ELEMENT SIMULATIONS

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ORIGINAL INVESTIGATION

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by this form of indentation loading in the experimental specimens,

for both Ecoflex 0030 and passive porcine muscle.

The results described above emphasized pressure as a function

of location within the specimen. The FE model results were also

compared against experimental data to examinehowpressure varied

with time at a given location. These results are shown in Figure 6.

As before, the results suggest good agreement between FE simu-

lations and the experimental pressure-time history produced during

the indentation tests at ‘‘deep’’ and ‘‘superficial’’ point locations in

the specimen. The results also confirm the finding that indentation

of Ecoflex 0030 generated higher pressure magnitudes than did

similar indentation of passive porcine muscle.

Linear regression (experiment vs model) of the indentation

pressure-time histories showed a high goodness of fit (R2 = 0.99,

P G .05) for both deep and superficial pressure in Ecoflex 0030. A

slightly weaker but still significant fit of the porcinemusclemodel

to the data (R2 = 0.849 and 0.92 for deep and superficial, respectively)

was seen.Deep pressure showed a slope near unity for both porcine

muscle (1.007) and Ecoflex 0030 (0.987). Superficial pressure data

showedslightlymore spread in slopevalues. ForEcoflex 0030, a slope

of0.777wascalculated.Theslopevalue for superficialpressure inporcine

musclewas elevated (2.29), indicating that themodel underpredicted

theexperimental value (0.97 vs2.42mmHgatmaximumindentation).

Patient Simulator. Thepreliminary trial of the simulator prototype

revealed a stress distribution pattern similar to that observed in the

indentation testing (Figure 7). When manual pressure was applied

over the instrumented sacral region, itwasobserved that pressures in

the deep tissue adjacent to the bony prominence were higher than

those recorded inmore superficial tissuenear the skin surface. It is not

Figure 6.

PRESSURES MEASURED IN EXPERIMENTS COMPARED AGAINST FINITE ELEMENT MODEL-PREDICTED PRESSURES,

FOR SILICONE AND MUSCLE INDENTATION TESTS

A, Ecoflex 0030 indentation test: deep and superficial pressures in relationship to time for both experimental and model data. B, Porcine muscle indentation test: deep and superficialpressures in relationship to time for both experimental and model data.

Figure 7.

RESULTS OF PRELIMINARY EXPERIMENTATION WITH

PATIENT SIMULATOR PROTOTYPE. PRESSURE IN

RELATIONSHIP TO TIME FOR SENSORS LOCATED AT DEEP

AND SUPERFICIAL LOCATIONS WITHIN THE PROTOTYPE

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possible tomake direct comparisons with the pressuremagnitudes

measured in the indentation experiments, because the depth of

the manually applied load was not recorded, and the geometric

configuration of the loading environment differed significantly from

that of the simplified indentation experiments.However, this prelim-

inary trial demonstrated qualitatively that silicone-based tissue an-

alogs were able to mimic the basic trend of a stress concentration

developing in thematerial in the region of a bony prominence,when

subjected to compressive loading.

DISCUSSIONTo address the increasing human and financial burden of DTIs,

it is crucial to train healthcare workers with the best techniques

available to preventDTI development. It is also necessary to provide

researcherswith suitable platforms for testingpressure-mitigating

products for DTI prevention. Particular attention must be paid to

deep tissue stresses in high-risk areas, such as the skin and soft

tissue over certain bony prominences associated with the pelvic

girdle and lower extremity, because 95%ofPrUsare known tooccur

on the lower half of the body.19

In this study, the authors characterized mechanical properties

of soft tissue analogs capable of generating shear moduli and stress

distribution trends similar to biological soft tissue. With these ana-

logs, the authors developed apreliminary patient simulator prototype

that could mimic the phenomenon of concentrated stress in deep

tissue near a selected bony prominence, the spinous tubercle of

the sacrum. The simulator was instrumented to provide real-time

feedback on local pressure conditions at different tissue depths. The

indentation experiments showed that, while the stress distribution

patterns in porcine muscle tissue paralleled those of the Ecoflex

0030 silicone, the stress magnitudes in silicone were substantially

higher than those inmuscle tissue. The clinical implications of this

discrepancy remain to be examined. Limitations of the current sim-

ulator prototype also include the fact that the interfaces between

the tissue layers (skin-fat, fat-muscle, muscle-bone interfaces) re-

quire further development to reflect anatomical structure and that

the model ultimately must be validated against biologic tissue rep-

resenting all tissue components covering a bony prominence.

In the long term, a fully developed and validated simulator, which

accuratelymimics all the relevant biomechanical complexities of human

anatomy, could be used as a research platform for testing the effects

of pressure-mitigating products on deep-tissue stresses. It could also

be used to educate healthcare professionals on proper positioning

techniques for deep pressure relief in the lower body. According

to the currentNational PressureUlcer Advisory Panel and European

Pressure Ulcer Advisory Panel International Guidelines for the

Prevention andTreatment of PressureUlcers,9 repositioning should

be utilized for all at-risk individuals. The panels assigned the highest

level of evidence (A) to this intervention.

It is well known that biological tissues exhibit viscoelastic mech-

anical behaviors such as creep, the phenomenon of increasing

deformation under constant load.14Y16,20,21 Although the use of a

viscoelastic material as a tissue analog would better capture this

biomechanical property of human tissues, it could also incur prac-

tical problems with the fabrication of a durable and reusable sim-

ulator. For instance, sustained loading could cause viscoelastic

materials to deform over time, such that recovery periods may be

neededbetween users to allow thematerial to return to its original

dimensions. Because of these limitations, silicone-basedmaterials

were selected as the best tissue analogs for the present study, be-

cause they could mimic tissue stiffness without the complicating

effects of time-dependent viscoelastic behavior.

All 3 silicone formulations had shear moduli values that fell

within the range of biological tissue, and Ecoflex 0030 and porcine

muscle demonstrated similar nonuniformstress distributionpatterns;

however, Ecoflex 0030 showedmuchhigher stressmagnitudes than

muscle under indentation loading. One of the factors that could

contribute to this difference is the large range of values for biolo-

gical soft tissue.Although the shearmodulusofEcoflex 0030 (22kPa)

fell within the range of passivemuscle (Table 1), it was on the upper

limits of this range. In contrast, the shearmodulus of porcinemuscle,

derived from the FE simulation, was found to be on the low end of

this range (~1kPa). This difference in stiffnesswould account for the

higher stressmagnitudes produced inEcoflex 0030under indentation

Figure 8.

FINITE ELEMENT MODEL SHOWING MESH PRIOR TO

INDENTATION TEST

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loading. Gefen et al8 have reported thatmuscle stiffness increases

in vivowith the development of deep PrUs. It would be informative

in future work to compare the stress distribution in silicone against

that of muscle tissue affected by DTI.

Biomechanical properties are largely dependent on test conditions.

For example, muscle demonstrates shear modulus temperature de-

pendence.23 In addition, examination of the shear moduli reported

in Table 1 shows that passive muscle is much less stiff than active

muscle. It has been shown previously that, in the human biceps

brachii, there is a linear relationship between shear modulus and

muscle load.22 This means that as themuscle activation increases,

its shear modulus increases. This suggests that the Dragon Skinma-

terial, although high within the range of the reported shear modulus

of relaxedmuscle tissues,maybea reasonable analog to the compres-

sivepropertiesofactivemuscleorevenmuscleunderpathogenesis.22Y25

Although it had a high shearmodulus, it was chosen as themuscle

simulant in the patient simulator prototype in order to account for

the significant stiffening that occurs under compression in in vivo

muscle tissue.8

Shear moduli of silicone rubbers and biological soft tissues

were compared (Tables 1 and 2) because shear modulus gives a

sense of the ‘‘feel’’ or stiffness of the material. However, in com-

paring the full stress-strain responses of the siliconeswith biological

materials, there is no perfect match. For example, none of the sili-

cone materials showed the same degree of strain hardening that

was observed byWu et al26 in their compression tests of skin and

adipose tissue. Based on other studies,27,28 it is expected that the

silicone rubbers would exhibit strain hardening at higher levels of

strain, yet this still differs from the strain hardening observed at

lower strain levels (0.3Y0.5) in biological tissues. Also significant to

this comparison is variation in species and anatomic location from

which the biological samples were taken, among the literature

studies used for benchmarking. Tissue properties vary from one

species to the next.Within a given species,material properties can

differ fromone location to another orwith temperature for the same

type of tissue.23 For instance, the fat that is found in the human foot

has a much different composition than fat found in other parts of

the body.29 This could explain discrepancies in strain hardening

between the fat data ofWu et al26 and those ofMiller-Young et al.29

In summary, the biomechanical behavior of human tissues is com-

plex, and results varywidely among studies. Siliconeswere not able

tomimic all the complex features of biological tissue biomechanics,

because of their significantly different structure and composition. In

the present study, it was found that the tested silicone formulations

were able tomimic certain features of tissue biomechanics that are

likely to be relevant for future simulator development, such as pos-

sessing shear moduli in the range of biological soft tissue and

exhibiting similar stress distribution patterns when subjected to

indentation loading. Much additional work is needed to examine

other biomechanical features, such as material density, appropriate

interface properties between different material layers, the influence

of fiber orientation onmusclemechanical properties, and the ability

of the simulated soft tissues to deform and return to their initial

configuration as joints are moved from one position to another.

CONCLUSIONSThis research represents a first step toward development of a pre-

clinical model simulating the biomechanical conditions of stress

and strain in deepmuscle, because local biomechanical factors are

acknowledged toplay a role inDTI initiation.6Y8,34,35 Future research

is needed to refine the capacity of preclinical models to simulate

biomechanical parameters in successive tissue layers ofmuscle, fat,

dermis, and epidermis typically intervening between bone and sup-

port surfaces, for body regions at risk for DTI.

In this study, materials used to simulate soft tissues were eval-

uated to characterize their behavior and compare with biological

soft tissues. Three formulations of silicone were found to have

shear moduli within the range of values for soft tissues published

in the literature. Pressure at various locations within the tissue was

measured to show the nonuniformpressure gradient that develops

within the tissue upon force application during indentation-type

loading, similar to that which occurs in deep muscle tissue com-

pressed against bony prominences.

Using this knowledge, a preliminary patient simulator prototype

was developed. Materials were selected to mimic the mechanical

properties ofmuscle, fat, and skin. The skeleton, moldedmuscles,

skin layer, and simulated fat were assembled, and miniature pres-

sure transducers were used to record local pressures in deep tissue

near the spinous tubercle of the sacrum and in superficial tissue,

above the spinous tubercle just beneath the skin.

A patient simulator that can mimic the biomechanical aspects

of DTI initiation, namely, stress and strain distributions in soft tis-

sues subjected to lifelikemechanical loading conditions, is needed

in the wound care industry. This future work will include extensive

further development andvalidationof thedevice design.Ultimately,

future iterations of this device could be used to train healthcare

professionals in best practices of lower body position for deep pres-

sure relief, which could greatly reduce the number of patients suf-

fering from DTI. The device would also be an innovative test

platform for evaluating the efficacy of products designed to prevent

PrUs, such as cushions, mattresses, and dressings.&REFERENCES

1. National Center for Injury Prevention and Control: CDC Injury Fact Book. Atlanta, GA: Centers

for Disease Control and Prevention; 2002.

2. Whittington K, Patrick M, Roberts J. A national study of pressure ulcer prevalence and

incidence in acute care hospitals. J Wound Ostomy Continence Nurs 2000;27:209-15.

3. Bouten CV, Oomens CW, Baaijens FP, Bader DL. The etiology of pressure ulcers: skin deep or

muscle bound? Arch Phys Med Rehabil 2003;84:616-9.

ADVANCES IN SKIN & WOUND CARE & FEBRUARY 201567WWW.WOUNDCAREJOURNAL.COM

ORIGINAL INVESTIGATION

Copyright © 2015 Wolters Kluwer Health | Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

Page 10: Use of Silicone Materials to Simulate Tissue …wcu.edu/WebFiles/PDFs/KS_Sparks_Tanaka.pdfUse of Silicone Materials to Simulate Tissue Biomechanics as Related to Deep Tissue Injury

4. Vidal J, Sarrias M. An analysis of the diverse factors concerned with the development of

pressure sores in spinal cord injured patients. Paraplegia 1991;29:261-7.

5. Gefen A. Bioengineering models of deep tissue injury. Adv Skin Wound Care 2008;21:30-6.

6. Linder-Ganz E, Shabshin N, Itzchak Y, Gefen A. Assessment of mechanical conditions in

sub-dermal tissues during sitting: a combined experimental-MRI and finite element approach.

J Biomech 2007;40:1443-54.

7. Linder-Ganz E, Gefen A. Mechanical compression-induced pressure sores in rat hindlimb:

muscle stiffness, histology and computational methods. J Appl Physiol (1985) 2004;96:

2034-49.

8. Gefen A, Gefen N, Linder-Ganz E, Margulies SS. In vivo muscle stiffening under bone

compression promotes deep pressure sores. J Biomech Eng 2005;127:512-24.

9. European Pressure Ulcer Advisory Panel and National Pressure Ulcer Advisory Panel. Pre-

vention and treatment of pressure ulcers: quick reference guide. Washington, DC: National

Pressure Ulcer Advisory Panel; 2009.

10. Lyder HC. Pressure ulcer prevention and management. JAMA 2003;289:223-6.

11. Garcia AD, Thomas DR. Assessment and management of chronic pressure ulcers in the

elderly. Med Clin North Am 2006;90:925-44.

12. Allen V, Ryan DW, Murray A. Repeatability of subject/bed interface pressure measurements.

J Biomed Eng 1993;15:329-32.

13. Sprigle S, Dunlop W, Press L. Reliability of bench tests of interface pressure. Assist Technol

2003;15:49-57.

14. Macosko CW. Rheology Principles, Measurements, and Applications. New York, NY: Wiley-VCH;

1994:5-136.

15. Bosboom E, Hessenlink MK, Oomens CW, Bouten CV, Drost MR, Baaijens FP. Passive trans-

verse mechanical properties of skeletal muscle under in vivo compression. J Biomech 2001;34:

1365-8.

16. Van Loocke M, Lyons CG, Simms C. Viscoelastic properties of passive skeletal muscle in com-

pression: stress-relaxation behaviour and constitutive modeling. J Biomech 2008;41:1555-66.

17. Then C, Menger J, Benderoth G, et al. A method for a mechanical characterisation of

human gluteal tissue. Technol Health Care 2007;15:385-98.

18. Anderson AE, Ellis BJ, Weiss JA. Verification, validation and sensitivity studies in computational

biomechanics. Comput Methods Biomech Biomed Engin 2007;10:171-84.

19. Dharmarajan T, Sugalino JT. Pressure ulcers: clinical features and management. Hosp

Physician 2002;38(3):64-71.20. Zahouani H, Pailler-Mattei C, Sohm B, Vargiolu R, Cenizo V, Debret R. Characterization of

the mechanical properties of a dermal equivalent compared with human skin in vivo by

indentation and static friction tests. Skin Res Technol 2009;15:68-76.

21. Ferry JD. Viscoelastic Properties of Polymers. 3rd ed. New York, NY: Wiley and Sons; 1980.

22. Dresner M, Rose GH, Rossman PJ, Muthupillai R, Manduca A, Ehman RL. Magnetic resonance

elastography of skeletal muscle. J Magn Reson Imaging 2001;269-76.

23. Sapin-de Brosses E, Gennisson JL, Pernot M, Fink M, Tanter M. Temperature dependence

of the shear modulus of soft tissues assessed by ultrasound. Phys Med Biol 2010;55:

1701-18.24. Lacourpaille L, Hug F, Bouillard K, Hogrel JY, Nordez A. Supersonic shear imaging provides

a reliable measurement of resting muscle shear elastic modulus. Physiol Meas 2012;33(3):

N19-28.25. Ringleb SI, Bensamoun SF, Chen Q, Manduca A, An KN, Ehman RL. Applications of magnetic

resonance elastography to healthy and pathologic skeletal muscle. J Magn Reson Imaging

2007;25:301-9.

26. Wu JZ, Cutlip RG, Andrew ME, Dong RG. Simultaneous determination of the nonlinear-elastic

properties of skin and subcutaneous tissue in unconfined compression tests. Skin Res Technol

2007;13:34-42.27. Shergold OA, Fleck NA, Radford D. The uniaxial stress versus strain response of pig skin

and silicone rubber at low and high strain rates. Int J Impact Eng 2006;32:1384-402.

28. Lee OS, Kim MS, Kim KJ, Hwang SW, Cho KS. Dynamic deformation behavior of rubber under

high strain rate compressive loading. Int J Mod Phys B 2003;17:1415-20.29. Miller-Young JE, Duncan NA, Baroud G. Material properties of the human calcaneal fat

pad in compression: experiment and theory. J Biomech 2002;35:1523-31.30. Abaqus: Abaqus User’s Manual (Version 6.10). Providence, RI: Dassault Systemes Simulia

Corp; 2010.

31. Boyce MC, Arruda EM. Constitutive models of rubber elasticity: a review. Rubber Chemistry

and Technology 2000;73:504-23.

32. Candadai RS, Reddy NP. Stress distribution in a physical buttock model: effect of simulated

bone geometry. J Biomech 1992;25:1403-11.

33. Reddy NP, Patel H, Cochran GV, Brunski JB. Model experiments to study the stress distributions

in a seated buttock. J Biomech 1982;15:493-504.

34. Linder-Ganz E, Engelberg S, Scheinowitz M, Gefen A. Pressure-time cell death threshold for

albino rat skeletal muscles as related to pressure sore biomechanics. J Biomech 2006;39:2725-32.

35. Bader D, Bouten C, Colin D, Oomens C, eds. Pressure Ulcer Research: Current and Future

Perspectives. Berlin, Germany: Springer-Verlag; 2005.

APPENDIXFinite element simulations were created using Abaqus software

(v6.12-1; Simulia, Providence, Rhode Island). All experiments were

modeled as axisymmetric, and elements of type CAX4R (4-node,

bilinear, axisymmetric, quadrilateralwith reduced integration)were

used. A typical FE mesh is shown in Figure 8. For uniaxial com-

pression test simulation, the bottom surface was constrained in the

vertical direction, and the appropriate amount of strainwas applied,

at the experimental strain rate, for each silicone formulationmodel.

For indentation testing, both the silicone and the porcine muscle

sampleswere constrained along the bottom in the vertical direction

and along the left edge in the horizontal direction. Each samplewas

loaded at a constant rate of 0.5 mm/s for 8 seconds.

Silicone rubber formulations andmuscle tissue17 weremodeled

as hyperelastic materials. The strain energy potential,U, was defined

using the Ogden model30 (Equation 1):

U ¼XN

i

2�i

�2i

ð ���i1 þ ��

�i2 þ ��

�i3 � 3Þ þ

XN

i

1

DiðJ � 1Þ2i

where �i, �i,N, andDi are material coefficients, ��j = Jj1/3 �j for j =

1,2,3, J is the volume ratio, and �j are the principal stretches. Of

interest for this work, the shearmodulusG can be calculated from

the �i coefficients as (Equation 2):

G ¼XN

i

�i

where N = 1 for silicone and N = 2 for muscle.17 The shear

modulus was used as one means to compare the mechanical

behavior of the various tissue analogs to that of native biological

tissues reported in the literature. Poisson ratio,�, can be calculated

from D1 and G as (Equation 3)17,30:

D1 ¼3

G

ð1� 2�Þð1þ �Þ

For additional detail on hyperelasticity, a review is given by

Boyce and Arruda.31

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